Actually, QM makes all the difference in the world; we really need the details of what electrons are doing to talk about chemistry. I’ll try to be brief, but…
It isn’t at all unreasonable to think of molecules as a bunch of atoms that interact only weakly, because this is indeed the case. And that’s the entire problem.
To elaborate a little, in my units[sup]1[/sup] the energies of quite strong chemical bonds are of order unity, while total energies of a molecule are several orders of magnitude larger.[sup]2[/sup] For instance, the total energy of the water molecule is about -76 Hartree; the total energy of all the atoms is about -75.8, and the chemical bonds therefore account for well under 0.5% of the total energy.
Clearly, the chemical bond is only a small perturbation to a molecule as a bunch of noninteracting atoms. But it’s chemical bonds that determine chemistry, of course, so we’re forced to look at the small difference of two numbers that are each several of orders of magnitude larger than the number we’re after. Clearly, no crude model can capture the small energy changes associated with chemical processes accurately enough to be useful; an error of even 1% in the total energy can mean errors of thousands of percent in energy differences. The only way I know of to treat chemical processes with any degree of predictive accuracy is to do hideously expensive QM.[sup]3[/sup]
Now, it’s relatively straightforward to calculate molecular geometry if I’m willing to pretend that molecules are a bunch of atoms connected by empirical forcefields. But if you ask for more than that, if you ask for ionization energies, or dissociation energies, vibrational frequencies, NMR coupling constants, or any of a whole host of other things an experimentalist might measure, you’re basically out of luck: you have to deal with the details of the electronic behaviour, and that means QM.
This makes a great deal of sense, because chemistry is, basically what happens when the electronic structure of a bunch of atoms changes (witness things like Lewis structures). So pretending that a molecule is a collection of atoms connected in some empirical way really means you can’t study most interesting chemical processes.
[sup]1[/sup] In quantum chemistry, we use units where the electronic charge, the electronic mass, and hbar are all equal to 1; our unit of energy (the Hartree) is thus twice the energy of the hydrogen atom. It’s a stupid system of units because everything is dimensionless, but it’s the convention.
[sup]2[/sup] To give a rough idea, the energy of an atom goes asymptotically as Z[sup]7/3[/sup], where Z is the atomic charge, if my memory isn’t failing me in my old age.
[sup]3[/sup] I’ve spent 8 hours on a Cray doing the helium atom, before, although to be fair my calculations are a lot more expensive than most, as I’m after numbers which are far more precise than we really need to worry about for most purposes.